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Higher Polytechnic University College
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Grao en Enxeñaría Naval e Oceánica
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The following topics develop the contents established in the tab of the Memoria de Verificación, which are: Statistical data analysis. Probability calculation. Point estimation and confidence intervals. Hypothesis testing. Introduction to statistical quality control.
Description of a statistical variable. General Concepts.
Frequency distributions.
Plots and data visualization.
Measurements of position, variability and shape.
Description of several statistical variables. Statistical vector.
Linear regression.
Probability. General Concepts.
Axiomatic definition of Kolmogorov.
Assigning probabilities: Laplace rule.
Conditional probability. Definition of conditional probability.
Independence of events.
Theorems of product, Bayes and law of total probability.
One-dimensional random variables. Concept of one-dimensional random variable.
Discrete and continuous random variables.
Transformation of random variables.
Typical measures of a random variable. Inequality of Tchebychev.
Probability distributions for discrete variables Discrete random variables: discrete uniform distribution.Bernoulli distribution. Binomial distribution. Geometric distribution. Negative binomial distribution. Poisson distribution. hypergeometric distribution
Probability distributions for continuous variables Probability distributions of continuous random variables: Normal distribution. The central limit theorem.Approximate (limit) relationships between probability distributions. Pearson's Chi-square distribution. Student's t-distribution. Fisher-Snedecor's F distribution. Other distributions.
Introduction to Statistical Inference. General concepts. Sampling. Generation of random variables. Point estimation concept. The sampling distribution of a point estimator.
Point estimation. Properties of the estimators. Methods of obtaining estimators. Point estimator of the mean. Point estimator of variance. Point estimator of a proportion.
Estimation of confidence intervals. Confidence interval concept. Confidence intervals for the mean. Confidence interval for variance. Confidence interval for a proportion. Confidence intervals for the difference of two means. Confidence interval for the quotient of two variances. Confidence interval for the difference of two proportions.
Hypothesis tests General concepts. Critical level (p-value) and significance level of a hypothesis test. Power of a test. General procedure for hypothesis testing. Tests for the mean. Test for variance. Test for a proportion. Tests for the difference of two means. Test for the ratio of two variances. Test for the difference of two proportions. Position Tests. Goodness of fit tests. Independence tests. Homogeneity tests.
Introduction to statistical quality control Basic concepts. Six Sigma Methodology. Main statistical quality control tools.
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